Tickets to a movie cost 5$ for adults and 3$ for students. A group of friends purchased 18 tickets for $82.00. How many Adults ticket did they buy?

Answer 1

Let's use algebra to solve this problem.

Let \( x \) be the number of adult tickets and \( y \) be the number of student tickets.

We have two equations based on the information given:

1. The total number of tickets purchased: \[ x + y = 18 \]

2. The total cost of the tickets: \[ 5x + 3y = 82 \]

Now we can solve these equations step by step.

From the first equation, we can express \( y \) in terms of \( x \): \[ y = 18 - x \]

Now we can substitute \( y \) into the second equation: \[ 5x + 3(18 - x) = 82 \]

Distribute the 3: \[ 5x + 54 - 3x = 82 \]

Combine like terms: \[ 2x + 54 = 82 \]

Subtract 54 from both sides: \[ 2x = 28 \]

Now divide by 2: \[ x = 14 \]

So, the number of adult tickets purchased is \( \boxed{14} \).

To check, we can find \( y \): \[ y = 18 - x = 18 - 14 = 4 \]

Now let's verify the total cost: \[ 5(14) + 3(4) = 70 + 12 = 82 \]

The calculations confirm that the solution is correct. Thus, they bought 14 adult tickets.